Accretion Flow Properties of three MAXI Black Hole Candidates:
Analysis with the TCAF Solution
Dipak Debnath,1 Sandip K. Chakrabarti,2,1 Arghajit Jana,1 D. Chatterjee1 A. A. Molla,1 S. Mondal3,11Indian Center for Space Physics, 43 Chalantika, Garia St. Rd., Kolkata, 700084, India.
2
S. N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata, 700098, India.
3
Instituto de Fı́sica y Astronomı́a, Universidad de Valparaı́so, Gran Bretana N 1111, Playa Ancha, Valparaı́so, Chile.
E-mail: dipak@csp.res.in (DD); chakraba@bose.res.in (SKC); argha@csp.res.in (AJ)
Abstract
Recently after the implementation of Chakrabarti and his collaborators Two-component advective flow
(TCAF) model into HEASARC’s spectral analysis software package XSPEC as an additive table model,
we found that it is quite capable to describe the underlying accretion flow dynamics around black holes
with spectral fitted physical parameters. Properties of diﬀerent spectral states and their transitions during
an outburst of a transient black hole candidate (BHC) are more clearly understandable. One can evenpredict frequency of the dominating quasi-periodic oscillations (QPOs) from the TCAF model fitted shock
parameters and even predict the most probable mass range of an unknown BHC from TCAF fits. This
gives us a confidence that the description of accretion process is more clear than ever before. Recently
we studied three MAXI/GSC discovered Galactic transient BHCs: MAXI J1659-152, MAXI J1836-194,
MAXI J1543-564, with the TCAF solution to study accretion flow properties of these compact objects
during their very first outbursts. We classified entire outbursts of these sources into diﬀerent spectral
states on the basis of nature of variations of TCAF model fitted physical flow parameters and observed
QPOs. Probable mass ranges of these BHCs are also estimated from our study. Estimation of X-ray jet
fluxes during the 2011 outburst of MAXI J1836-194 are also done.
Key words: X-Rays:binaries – stars individual: (MAXI J1659-152, MAXI J1836-194, MAXI J1543564) – stars:black holes – accretion, accretion disks – ISM: jets and outflows – radiation:dynamics

1.

Introduction

Transient black hole candidates (TBHCs) are very interesting objects to study in X-rays as they exhibit
rapid evolutions in their temporal and spectral properties during outbursts, which are strongly correlatedwith each other. Several works are present in the literature (see, e.g., Debnath et al., 2008, 2013 and references therein), which explain variations of spectral
and temporal properties of these objects during their
X-ray outbursts. In general, it has been found thatthese objects exhibit diﬀerent spectral states, such as
hard (HS), hard-intermediate (HIMS), soft-intermediate(SIMS) and soft (SS) during their outbursts. They also
exhibit low and high frequency quasi-periodic oscillations(QPOs) in some of these spectral states (see, Debnath
et al. 2013 and references therein). The frequencies of
QPOs are found to evolve with time during the rising anddeclining phases (more precisely, during hard and hardintermediate spectral states) of the outbursts. According to the nature of the variations of temporal and spec-

tral properties during outbursts, we can classify transient
BHCs into two types: i) type-I or classical-type, where
all spectral states are observed (HS ⇀↽ SS via two intermediate, HIMS and SIMS spectral states), and ii) type-IIor harder-type, where SS (sometimes even SIMS) could
not been observed. The type-II type of outbursts are
generally termed as ‘failed-outbursts’.
It is well known that emitted spectrum of the radiation coming from BHCs is a multi-color in nature, andcontains both thermal and non-thermal components.
One component is basically the multi-color blackbody
radiation from the standard Keplerian disk (Shakura& Sunyaev 1973), and the other is a power-law component, which is originated from the ‘Compton’ cloud(Sunyaev & Titarchuk 1980) composed of hot electrons,
which is cooled down due to repeated Compton scattering of softer (lower energy) photons. In the two component advective flow (TCAF) solution of Chakrabarti& Titarchuk (1995; hereafter CT95), the role of socalled ‘Compton cloud’ or ‘hot corona’ is replaced by theCENtrifugal pressure supported BOundary Layer (CENBOL), which automatically forms behind the centrifugal barrier due to piling up of the low viscosity (subcritical) and low angular momentum optically thin matter, known as sub-Keplerian (halo) accretion component.
In TCAF, the other component of accretion flow is thehigh viscous, optically thick and geometrically thin Keplerian (disk) component which is submerged inside thehalo component. CENBOL being much hotter in general, the Keplerian disk is naturally truncated at theshock location close to the black hole. This Keplerian
flow settles down to a standard SS73 disk when coolingis eﬃcient. Low energy (soft) thermal photons from the
Keplerian disk intercept with the CENBOL (composedof hot electrons) and emit as high energy (hard) photons
by cooling down CENBOL through repeated Compton
scatterings.
Recently, in 2014, Debnath and his collaborators
have successfully been implemented TCAF solution into
HEASARC’s spectral analysis software package XSPEC
as an additive table model to fit black hole spectrum.
After that, they have been quite successful to explain accretion flow properties of few transient BHCs (such as,
GX 339-4, H 1743-322, Swift J1753.5-1027, other than
three MAXI objects, MAXI J1659-152, MAXI J1836194, MAXI J1543-564) during their X-ray outbursts(Debnath et al., 2014; 2015a,b, 2017; Mondal et al.,2014; Jana et al., 2016; Chatterjee et al. 2016; Molla
et al. 2016, 2017; Bhattacharjee et al. 2017). From
the TCAF model fitted spectrum, one can not only directly obtain information about the instantaneous accretion rates of the two components (Keplerian disk rate ṁdin ṀEdd and sub-Keplerian halo rate ṁh in ṀEdd ), butalso obtain crucial information on shock parameters (instantaneous shock location Xs in Schwarzschild radiusrg =2GM/c2 , and shock compression ratio R), which allows us to estimate frequencies of the dominating QPOs
(if observed in PDS; see, Debnath et al. 2014). Depending upon the variations of accretion rate ratio (ARR =halo/disk rates) and nature of QPOs (shape, frequency,
Q value, rms%), classification between diﬀerent observed
spectral states and their intermediate transitions are wellunderstood. A strong correlation between the spectral
and timing properties during the outburst period in theform of hysteresis loop, i.e, in ARR-intensity diagram(ARRID) was observed, where diﬀerent spectral states
are found to be correlated with diﬀerent branches of the
diagram (see, Jana et al. 2016). Most probable mass
(MBH ) ranges of MAXI J1659-152, MAXI J1836-194,
MAXI J1543-564, H 1743-322, etc. have been predictedfrom our spectral analysis with TCAF model fitted constant normalization (N ) method (see, Molla et al. 2016,2017; Jana et al. 2016; Chatterjee et al. 2016; Bhattacharjee et al. 2017).

In this Conference Proceeding, we will briefly discuss
about the accretion flow properties of three MAXI objects (MAXI J1659-152, MAXI J1836-194, MAXI J1543564) during their very first outbursts after discovery, obtained from our spectral and temporal analysis under
TCAF paradigm (Debnath et al. 2015; Molla et al. 2016;
Jana et al. 2016, 2017; Chatterjee et al.2016).
2. MAXI J1659-152: (Debnath et al. 2015b; Molla etal. 2016)
The source was discovered by MAXI/GSC on 2010 Sep.
25 at R.A.= 16h 59m 10s , Dec = −15◦ 16′ 05′′ (Negoro etal. 2010). It is shortest orbital period (2.414 ± 0.005 hr)
BH with acceptable ranges of distance, inclination angle,
mass are 5.3−8.6 kpc, 60◦ −80◦ , 3−8 M⊙ respectively. In
Debnath et al. (2015b), we studied both the spectral andtiming properties of the source during its 2010 outburst
by analyzing 2 − 25 keV RXTE/PCA data of 30 observational IDs, starting from 2010 Sep. 28 (MJD=55467)
to 2010 Nov. 11 (MJD=55508). 2.5 − 25 keV spectra are
fitted with TCAF model fits file by keeping all model
parameters (ṁd , ṁh , Xs , R, N ) as free, except MBH
was kept frozen at 6 M⊙ . Depending upon the variations of ARR and nature of QPOs, we classified entire
2010 outburst into three spectral states (HS, HIMS and
SIMS) in the sequence of: HIMS (Ris.)→SIMS→HIMS(Dec.)→HS (Dec.). On the first PCA observation day,source was already in HIMS (Ris.). Monotonic evolutions of low frequency QPOs during HIMS (Ris.) and
HIMS-HS (Dec.) are observed and during the SIMS,QPOs are observed sporadically. No, signature of SS isobserved during the outburst, which may be due highsupply of low viscous halo matter both via accretion andwind, since it is a short orbital period BH.
In Molla et al. (2016), we refitted all spectra by keeping TCAF model normalization (N ) in a fixed value(which is the average N value of the fitted normalizations, when all parameters were kept free) to estimate
probable mass range of the source as 4.7 − 7.8 M⊙ . We
also verified this mass range with the estimated mass
value (5.1−7.4 M⊙ ) obtained from declining phase QPO
frequency evolution, fitted with propagating oscillatory
shock (POS) model (Chakrabarti et al. 2005, 2008; Debnath et al. 2010, 2013; Nandi et al. 2012). Finally, combining estimated mass ranges obtained from TCAF and
POS models, we obtained a most probable mass rangeof the source as 4.7 − 7.8 M⊙ or 6+1.8−1.3 M⊙ .
3. MAXI J1836-194: (Jana et al. 2016)
This short orbital period (< 4.9 hr), low inclination angle (4◦ − 15◦ ) angle and highly rotating (a = 0.88 ± 0.03)
BH was discovered on 2011 Aug. 29 simultaneously by
SWIFT/BAT and MAXI/GSC (Negoro et al. 2011a) at
R.A. = 18h 35m 43s .43, Dec = −19◦ 19′ 12′′ .1. Cenko etal. (2011) reported companion as a high massive B[e]star. The probable mass and distance of object werereported as 4 − 12 M⊙ , 4 − 10 kpc respectively. The
source was highly active in radios. In Jana et al. (2016),
we studied spectral and timing properties of the source
using RXTE/PCA data of 35 observational IDs starting from 2011 Aug. 31 (MJD=55804) to 2011 Nov. 24(MJD = 55889). 2.5 − 25 keV spectra are fitted with
TCAF model fits file to extract physical flow parameters.
Low frequency QPOs are observed sporadically throughout the outburst with a general trend of increasing nature of frequency during the rising phase and decreasing
nature of frequency during declining phase. Depending
upon the variations of TCAF model fitted flow parameters, ARRs and nature of QPOs, we classified entire
2011 outburst of the source into two harder states (HSand HIMS). These spectral states are observed in the sequence of: HS (Ris.)→HIMS (Ris.)→HIMS (Dec.)→HS(Dec.). We divided HIMS into two classes, since during
the HIMS (Ris.), ARR decreased due to decreasing nature of ṁh and increasing trend of ṁd . On the transition
day between two HIMS (MJD=55820), ARR becomesminimum (due to maximum value of ṁd , and minimum
value of ṁh ) with maximum value of the observed QPOs.
After that ARR increased and becomes maximum on thetransition day between HIMS (Dec.) to HS (Dec.) due torise in ṁh . There after during HS (Dec.), ARR decreased
due to fall of both rates. During entire 2011 outburst,
no signature of softer spectral states (SS and SIMS) are
observed, which may be due to high supply of low viscous wind matter, since BH accretion disk is immersed
inside the excretion disk of the B[e] companion.
To find correlation between spectral and timing properties, we draw ARRID and compared it with hardnessintensity diagram (HID; Debnath et al. 2008 and references therein). In ARRID (see, Fig. 4 of Jana et al.
2016), we plotted 2 − 25 keV PCA count rates as a function of ARR. Diﬀerent observed spectral states and theirtransitions are found to be more prominent in ARRID
compared to HID (N.B.: point D, where transition between declining HIMS and HS is feasible only in ARRID). Observing peak diﬀerences between disk and halo
rates during the entire outburst, we predicted viscoustime scale as ∼ 10 days. From our detailed spectral
study with the TCAF solution, we also estimated probable mass range of the source as 7.5 − 11 M⊙ , since inthe model mass is an input parameter. In Jana et al.
(2017), we also calculated X-ray jet fluxes from spectral
analysis using TCAF solution.

of the source using spectral fits with combined diskbb
and simpl models, where as in Chatterjee et al. (2011),
we studied initial rising phase of the outburst with the
TCAF solution. We analyzed initial seven observationsof RXTE/PCA in the rising phase of the outburst, starting from 2011 May 10 (MJD=55691.09) to 2011 May
15 (MJD=55696.66). On the first observation day, thesource was already in HIMS. From the nature of the variations of TCAF model fitted physical flow parameters,
ARRs and QPOs, during we classified our observation
period into two intermediate spectral states, HIMS and
SIMS. Low frequency QPOs are observed during first six
observations. During initial five observations a monotonic evolution (increasing trend) of type-C QPOs (from1.05− 5.70 Hz) is observed and on sixth day, it decreased
to 5.08 Hz. We defined fifth observation as the transition
day between two outbursts. From TCAF model fits, Keplerian disk rate (ṁd ) increased as outburst progressed,
where as sub-Keplerian halo rate (ṁh ) decreased initially upto the transition day and then slightly increased
for last two observations. Shock is found to move inward with decreasing strength. Evolution of QPOs during HIMS, was also independently fitted with the POS
model and instantaneous shock location and compression ratios are calculated, since according to the POS
model, QPOs occur due to oscillation of the same shock(forms at the outer edge of the CENBOL) which we use
in TCAF model code. We also predicted frequency of theobserved type-C QPOs from TCAF model fitted shock
parameters to compare those with observed and POS
model fitted values, using the following relation,

where, νs0 is the first observed QPO frequency and tinf allis the infall time.
In Chatterjee et al. (2016), we also estimated probablemass range of the source from our spectral and temporal
analysis with the TCAF solution and the POS model
respectively. From TCAF model spectral fits, MBH wasobserved in the range of ∼ 13.5−14.0 M⊙ , where as fromthe POS model fitted QPO frequency evolution MBH
was found at 13 M⊙ for the best-fit (χ2red =0.90). Thenwe varied MBH in POS model code for both positive andnegative values and observed, for 90% confidence (χ2red ≤2.7) allowed mass range could be ∼ 12.6−13.6 M⊙ . Then
finally combining results obtained from both TCAF and
POS models, we predicted mass range of the source as∼ 12.6 − 14.0 M⊙ or 13+1.0−0.4 M⊙ .

4. MAXI J1543-564: (Chatterjee et al. 2016)
The source was discovered by MAXI/GSC on 2011 May
8 at R.A.=15h 43m 9s .12 and Dec.=56◦ 25′ 15′′ .6 (Negoro
et al. 2011). Stiele et al. (2011) studied entire outburst

5. Discussions and Concluding Remarks
We studied spectral and temporal properties of three
MAXI observed BHCs during their very first outbursts
after discovery using RXTE/PCA data. Out of them

3

νs0
c
1
νQP O = tinf
= 2GM
1/2 ] ,
BH [R Xs (Xs −1)
alltwo (MAXI J1659-152 and MAXI J1836-194) are shorter
orbital period BHCs, where soft states were missing.
These short orbital period sources belongs to a special
category (type-II or harder-type) of sources (for e.g.,
XTE J1118+480, Swift J1753-0127, etc.) where accretion disks are dominated with the low angular momentum sub-Keplerian halo matters. During the outbursts,
Keplerian disk rate does not rises much compared to thehalo rate, such that it is able to cool down CENBOL
completely. On the other hand, MAXI J1543-564 is a
type-I or classical-type, where all spectral states are observed (see, Stiele et al. 2011).
Spectral fits of these three MAXI objects with the
TCAF solution, provide us a direct evidence of two components accretion flows as they are observed to vary independently during the outbursts. Spectral study with
the TCAF solution enables us not only to understandspectral properties of the BHCs but also to predict othertiming and physical parameters associated with the BHs.
Diﬀerent spectral states and their transitions from one
state to another are more clearly understandable fromthe variations of TCAF model fitted physical flow parameters and nature of QPOs. Frequency of the dominating
type-C QPOs also could be predicted from TCAF model
fitted shock parameters, since in TCAF we use same
shock, whose oscillation is believed to the fact of QPOs.
In ARRID, we saw that the correlation between spectral
and timing properties of transient BHCs is more fundamental than so-called ‘q’-diagram or HID. We also estimated probable mass range of the three MAXI sourcesfrom our TCAF model fitted spectral analysis within agood accuracy. We also estimated X-ray jet fluxes during
the 2011 outburst of MAXI J1836-194 from our spectral
study with the TCAF solution (see, proceeding of Janaet al. in this volume and Jana et al. 2017).
From our recent study of various BHCs with the
TCAF solution including three MAXI objects discussed
here, we can say that TCAF is the most accurate theoretical model to understand physics of accretion processes
around a black hole, which was our decade long conjecture. Spectral fits with the model, not only explains
spectral properties and but also capable to explains various timing features including QPOs of BHCs. One canalso estimate physical source parameters, such as mass,
spin from spectral fits with the TCAF model. Finally, it
is needed to mention that we require only six model input parameters including the mass of the black hole andnormalization to fit a spectrum with the TCAF solution.
Acknowledgments
D.D. and D.C. acknowledge support from DST
sponsored Fast-track Young Scientist project fund
(SR/FTP/PS-188/2012). A.J. and D.D. acknowledges
support from ISRO sponsored RESPOND project fund

(ISRO/RES/2/388/2014-15).
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